Verification methods and agronomic enhancements for carbon removal based on enhanced rock weathering

ABSTRACT

The present disclosure relates to methods of verifying enhanced rock weathering using immobile trace elements found within a mineral amendment. Further disclosed are mineral amendments that enable enhanced rock weathering.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional patent application of U.S. Non-Provisional patent application Ser. No. 17/846,838, filed Jun. 22, 2022 which claims the priority benefit of U.S. Provisional Patent App. Ser. No. 63/322,672, filed Mar. 23, 2022; U.S. Provisional Patent App. Ser. No. 63/289,395, filed Dec. 14, 2021; and U.S. Provisional Patent App. Ser. No. 63/213,398, filed, Jun. 22, 2021; each of the foregoing of which are incorporated herein by reference in their respective entireties.

BACKGROUND

The last several years have witnessed a maturation of carbon markets from lightly scrutinized voluntary markets largely serving to provide positive marketing collateral to familiar consumer brands to rigorous compliance markets with proof-of-performance requirements often involving government and quasi-governmental regulators. There have also been a number of comprehensive proposals for decarbonization of the entire US economy, combining energy production, transportation, cement production, and agriculture. These proposals have included carbon dioxide removal (CDR) techniques as an essential component of the decarbonization plan, with a supportive ecosystem of science, policy, and project evaluation criteria. Within the diverse scope of decarbonization efforts, including renewable energy, biofuel, nature-based solutions, and more technical CDR techniques like direct air capture (DAC), The Oxford Principles have developed a taxonomy for categorizing diverse decarbonization strategies. This taxonomy distinguishes between avoided emissions (for instance, conversion of fossil fuel power to renewable power) and negative emissions (for instance direct air capture); distinguishes between avoided emissions that require storage (for instance carbon capture from a point source and sequestration into the ground) and those that do not require storage (the conversion to renewable energy); and the duration of the storage if so required (for instance, short lived forest carbon sequestration from delayed harvests versus storage of captured carbon in geological formations).

A number of for-profit and non-profit organizations have emerged that employ the Oxford Principles to evaluate proposals, particularly around the rigorous quantification across categories (Table 1). This, in essence, is the scorecard that projects will have to compete on to find acceptance in the industry. All other things equal, cost ends up being the primary driver, but quality is also a key consideration. Thus, historically buyers have been drawn to nature-based solutions that cost between $5-20/tCO₂ e (e.g., Corteva Carbon, Indigo Carbon), versus direct air capture projects that cost >$500/tCO₂ e (e.g., ClimeWorks). However, there are challenges to these nature-based solutions: recently these nature-based solutions have been subject to intense scrutiny for “gaming” the rules or otherwise failing to deliver prospective rewards. Among the technological solutions, there are a different set of challenges: rigor has been strong, but the reduction in price proportional to increase in deployment has been slow, and the ultimate price of DAC is not expected to drop below $150/tCO₂e (Keith et al 2018, https://doi.org/10.1016/j.joule.2018.05.006). In light of these challenges, we have developed a technology around “enhanced rock weathering” (ERW), in which silicate minerals are weathered in acidic soil solution, thus driving the uptake of additional CO₂ into dissolved inorganic carbon (DIC) in the soil solution. Our experimental work, life cycle analysis, and techno-economic modeling have indicated that ERW provides the permanence, additionality, and rigorous quantification of a DAC project, the large volume of a carbon capture and storage (CCS) project, and the unit economics of a nature based solution, thus creating a new tool to meet net-zero goals.

Details of Enhanced Rock Weathering

In “enhanced rock weathering” (ERW), silicate minerals are weathered by CO₂ from the ambient air which has been dissolved into water, reacting to produce dissolved inorganic carbon that is ultimately stored in the ocean as depicted in FIGS. 1 and 2 .

Background Geochemistry

The role of silicate rock weathering in maintaining the CO₂ balance of the atmosphere has been recognized for decades, first outlined by renowned chemist Harold Urey in the 1950's. The basic premise of the Urey reaction is that continental collisions release CO₂ to the atmosphere from volcanoes, and bring Mg- and Ca-bearing silicate rocks to the surface. The rainwater (H₂O) that falls upon these rocks is mildly acidic, as atmospheric CO₂ has dissolved in it and formed carbonic acid (H₂CO₃). For forsterite, the weathering reaction takes place following the form:

Mg₂SiO₄+4 H₂O+4CO₂→2 Mg₂++4 HCO₃ ⁻+4 H₄SiO₄

In this reaction, one mole of forsterite consumes four moles of CO₂, so two negatively charged bicarbonate HCO₃ ⁻ are created for every one divalent Mg²⁺ weathered. Given the molecular weight of forsterite (140 g/mol) and the molecular weight of CO₂ (44 g/mol), weathering one metric ton of forsterite removes 1.25 metric tons of CO₂ from the atmosphere. In general, such a formula can be used to define the “mineral potential” of a silicate based on its elemental composition:

$\begin{matrix} {{{MP} \equiv \frac{{t{CO}}_{2}e}{tOre}} = {{\frac{MW_{CO_{2}}}{100\%} \cdot \left( {\frac{{Mg}\%}{MW_{Mg}} + \frac{{Ca}\%}{MW_{Ca}}} \right)}*V}} & \left( {{Equation}1} \right) \end{matrix}$

where V is the valence of the cation (2 for Mg and Ca) and MW is the molecular weight.

The rate of weathering is determined by the surface area of the mineral, the acidity (pH) of the soil solution, the temperature of the solution, the availability of CO₂ reagent in solution, and the rate of removal of the reaction products by water. One of the key insights into the potential of “enhanced” rock weathering is that the rate of reaction, and thus CO₂ removal, can be greatly accelerated by increasing the surface area by pulverization into a fine powder (e.g., less than 100 um), incorporating into an acidic environment (e.g., pH less than 6) with abundant CO₂ present, and with steady water flux to remove reaction products to maintain acidity. While this formula defines the potential amount of CO₂ that may be removed by weathering, it does not speak to the rate; ancient rock formations testify that the rate of weathering can be extremely slow.

The relationship between silicates (like Mg₂SiO₄) and dissolved carbonates (like HCO₃ is not necessarily intuitive, as the carbonate system of water involves a number of coupled reactions. Atmospheric CO₂ dissolves into water according to an exchange coefficient:

CO_(2(aq))=H₂CO₃=K_(CO) ₂ *P_(CO) ₂

Technically pCO₂ is “fugacity” that represents its activity, but, as used herein, it is more or less equivalent to its partial pressure, and K_(CO) ₂ is the Henry's law coefficient that determines the aqueous CO₂ in equilibrium with the atmosphere. This aqueous CO₂ in turn hydrates with H₂O to become carbonic acid (H₂CO₃)′ which dissociates to become bicarbonate (HCO₃ ⁻) and carbonate (CO₃ ²⁻):

H₂CO₃↔HCO₃ ⁻+H⁺

HCO₃ ⁻↔CO₃ ²⁻+H⁺

These equilibrium reactions are defined by K1 and K2, the first and second carbonate system dissociation constants. pK1 and pK2 are about 5.9 and about 9.4 at STP, so greater than 99% of the charge in the dissolved carbonates is HCO₃ ⁻.

The carbonates are the largest constituents of total alkalinity, which is defined as the charge imbalance between weak acids (proton acceptors) minus proton donors:

TA=[HCO₃ ⁻]+2·[CO₃ ²⁻]+[OH⁻]−[H⁺]

There is an alternative definition of total alkalinity as the charge imbalance between conserved cations and conserved anions:

TA=[Na⁺]+2[Mg²⁺]+2[Ca²⁺]+[K⁺]+ . . . −[Cl⁻]−2[SO₄ ²⁻]−[NO₃ ⁻]

These two expressions are always equal (i.e. the charges balance). This means that an added Mg or Ca into soil solution will increase in HCO₃ ⁻ to balance the charge. We describe an analytical solution to compute how much carbon is taken up per unit of additional Mg or Ca. If we first define DIC as the sum of H₂CO₃, HCO₃ ⁻, and CO₃ ²⁻, and make use of the equilibrium equations above (defining H⁺ as “h” and H₂CO₃ as “s”):

${DIC} = {s \cdot \left\lbrack {1 + \frac{K_{1}}{h} + \frac{K_{1}K_{2}}{h^{2}}} \right\rbrack}$

And formulate TA using the same convention:

${TA} = {{s \cdot \frac{K_{1}}{h}} + {s \cdot 2 \cdot \frac{K_{1}K_{2}}{h^{2}}} + \frac{K_{w}}{h} - h}$

With these definitions in place, we can develop an estimate of dDIC/dTA. First, we compute the derivative dTA/dh:

$\frac{dTA}{dh} = {{{- s} \cdot \left( {\frac{K_{1}}{h^{2}} + {4 \cdot \frac{K_{1}K_{2}}{h^{3}}}} \right)} - \frac{K_{w}}{h^{2}} - 1}$

Next we compute the derivative dDIC/dh:

$\frac{dDIC}{dh} = {{- s} \cdot \left( {\frac{K_{1}}{h^{2}} + {2 \cdot \frac{K_{1}K_{2}}{h^{3}}}} \right)}$

Finally we multiply dDIC/dh by the inverse of dTA/dh to calculate dDIC/dTA:

$\frac{dDIC}{dTA} = {\frac{dDIC}{dh} \cdot \frac{dh}{dTA}}$

At the pH found in soils, each Mg or Ca is matched by two carbon atoms. In all circumstances, raising alkalinity results in increased pH. This is particularly important in marine settings, where ocean acidification from increased atmospheric CO₂ can be ameliorated by this export of alkalinity from land.

The potential for ERW as a commercial enterprise is limited by some fundamental issues:

-   -   A. The total amounts of mineral transformation and carbon         removal should be verifiable empirically. The verification         methods described below may be low cost at scale, can be         performed at arm's length by a 3rd party, and may have         safeguards to eliminate fraud.

Additionally, the commercial potential for ERW could be enhanced by a number of different features. Embodiments may include:

-   -   B. Processes and modifications of the engineered mineral product         that enhance the agronomic performance and ecosystem co-benefits         of the engineered mineral.     -   C. Processes and modifications of the engineered mineral product         that control or enhance the mineral dissolution rate of the         engineered mineral in soil environments and thus the rate of         removal of CO₂.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing illustrating the enhanced rock weathering cycle.

FIG. 2 is a graph depicting the effect of comminution on dissolution kinetics for a silicate.

FIGS. 3A to 3D are graphs depicting the kinetics for a particle size distribution of a pulverized silicate with median particle size of 80-100 um which closely approximates the alkalinity release dynamics for aglime.

FIG. 4 is a drawing illustrating the general scheme for a verified enhanced rock weathering cycle.

DETAILED DESCRIPTION

Summary: The following described methodologies can establish one version of a verification scheme that will demonstrate the transformation of the applied rock material and the subsequent carbon removal into secure geologic reservoirs as evidenced by observations collected from the soil. One set of methods (A) can measure the production of free ions from the applied material and the transport of those ions outside of a control volume as a direct measure of the amount of weathering and thus total carbon dioxide equivalent isolated from the atmosphere. Furthermore, as the elemental inputs into the soil induced by enhanced rock weathering can have significant effects on the soil geochemistry, methods in (B) describe systems and versions that can enhance the agronomic performance of the soil amendment and increase ecosystem co-benefits. Lastly, methods in (C) elaborate on versions that control and enhance the mineral dissolution rate, which increases the financial performance of enhanced rock weathering technology in the marketplace.

-   -   A. Systems and methods for monitoring and verification:         -   Described below are several example methodologies for             quantifying the rate and extent of mineral transformation             and carbon removal, which are referred to as “verification             methodologies”.         -   1. Example Verification Methodology 1:             -   a. A cation exchange resin and/or an anion exchange                 resin are packaged into a physical embodiment (such as a                 5 cm diameter tube, 5 cm in length, placed 30 cm below                 the soil surface) that allows vertical transport of                 fluids but not horizontal transport.             -   b. Commercial ion exchange resins are pre-equilibrated                 in such a way that their selectivity is high for the                 relevant ions, but their capacity is also sufficiently                 high such that saturation is minimized. This technology                 may allow for effective deployment for long periods of                 time, allowing passage of up to 4000 mm of moisture                 through the tube, without becoming saturated with                 respect to the ions of interest.             -   c. The ions of interest are restricted to divalent                 cations (Mg²⁺, Ca²⁺), carbonate species (HCO₃ ⁻ and CO₃                 ²⁻), and silicic acid (H₄SiO₄), important weathering                 products of preferred mineral soil amendments, such as                 ultramafic rocks, blast furnace slag, and other                 naturally occurring or industrial silicate minerals with                 high Mg and Ca content.             -   d. Three pre-equilibrated tubes are emplaced fully under                 the soil below a control depth (e.g., 30 cm, a typical                 depth of cultivation). This may be done by removing the                 top 30 cm soil with a shovel or auger, then gently                 placing the tube in the created void space. Following a                 certain period of time post-surface application of                 mineral soil amendment (e.g., 9 to 12 months after                 application), the tubes are retrieved, and the ions                 captured within the resin exchanges are measured using                 standard methodologies, such as ICP-OES and ICP-MS based                 concentration measurements. Three tubes are used to                 determine standard deviation error in triplicate.             -   e. By the principle of charge balance and known                 thermodynamic reactions taking place in the top 30 cm of                 soils, the amount of carbonate can be inferred purely                 from the measurement of cations, under certain                 assumptions and auxiliary geochemical data. By the                 addition of more specific anion exchange resins, such as                 styrene-divinylbenzene, these assumptions can be avoided                 to get a more precise answer. The increase in cation                 concentration in the subsurface soil pore water allows                 for the stoichiometric determination of carbon removal                 from the gas phase (ambient air).             -   f. The total carbon dioxide removed during the                 deployment period may be estimated as equal to the                 molecular mass of CO₂ (44 g/mol) multiplied by the sum                 of the number of moles of carbonate and two times the                 number of moles of bicarbonate, multiplied by the area                 on which mineral was applied to the field, divided by                 the cross-sectional area of the tube.             -   g. Direct measurement of aqueous bicarbonate and                 carbonate species, which are the most readily available                 forms of carbon induced by a gas exchange of carbon                 dioxide with the soil pore water, may be conducted using                 the specified anion exchange resin above. The expression                 as described in clause (f) explains the calculation used                 to convert this direct measurement of carbon to an                 absolute value of carbon dioxide removed during a                 specified application period.             -   h. Verification methodology 1 has the advantage that it                 can provide a direct measure of carbon flux and employs                 a measurement technique that is mature.             -   i. However, potential disadvantages may include the need                 for manufacturing (and its attendant demand for working                 capital); devices may occasionally be defective;                 emplacement of a device may alter the flow paths of                 water, which in turn alters the inferred ion fluxes;                 emplacement of a device may depend on the user; the                 knowledge of the location of emplacement may invite                 manipulation by a stakeholder involved in a carbon                 transaction; and others.         -   2. Example Verification methodology 2:             -   a. The principle behind Verification methodology 2 is                 that minerals applied for purposes of enhanced rock                 weathering contain, in addition to the elements outlined                 above that participate in the weathering reaction (i.e.,                 magnesium, calcium, iron, silicon, oxygen, hydrogen),                 additional elements in trace amounts. These additional                 trace elements (TEs) might include rare earth elements                 (REEs), rare metals (RM), other transition metals (TMs),                 or a combination thereof. Unlike the primary weathering                 products that are readily dissolved in solution and lost                 by leaching, some TEs are strongly bound to mineral and                 biological surfaces and do not readily leach from the                 soil control volume (e.g., the top 10 to 30 cm of soil),                 and are not removed by plants at the concentrations                 present in our applied rock. These strongly bound trace                 elements are referred to herein as immobile trace                 elements (ITEs). Thus, a measure of cumulative cation                 flux and carbon removal can be computed by comparing the                 ratio of the lost weathering products, such as                 magnesium, to ITEs, after accounting for background                 concentrations of ITEs in the initial soil.             -   b. As used herein, rare earth elements include scandium                 (Sc), yttrium (Y), lanthanum (La), cerium (Ce),                 praseodymium (Pr), neodymium (Nd), samarium (Sm),                 europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium                 (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium                 (Yb), lutetium (Lu) or a combination thereof. As used                 herein, rare metals include beryllium (Be), cesium (Cs),                 gallium (Ga), germanium (Ge), hafnium (Hf), niobium                 (Nb), rubidium (Rb), tantalum (Ta), zirconium (Zr), or a                 combination thereof. As used herein, transition metals                 include nickel (Ni), chromium (Cr), and zinc (Zn) among                 others and may include a combination of transition                 metals.             -   c. An approach based on ITEs depends on the degree of                 immobility of the element in soil environments, the time                 horizon after which the ITEs will be measured to                 estimate carbon removal, the abundance of ITEs in both                 the soil and the mineral added, and the analytical                 chemistry used to measure this abundance. An analytical                 technique that has low detectability thresholds for                 slightly mobile elements could be sufficient for                 relatively abundant (e.g., parts per thousand to parts                 per million) elements over short time horizons (e.g.,                 weeks to months). On the other hand, a different                 analytical technique could be used over longer time                 horizons, which in turn could involve quantification of                 very immobile elements that are present in much lower                 abundance (e.g., parts per billion to parts per                 trillion). The approach may be chosen based at least in                 part on cost, which ITEs are actually conserved, over                 which time horizons, as well as the performance of the                 analytical performance used.             -   d. The relative proportions of ITEs in a sample (rock or                 soil) constitute a type of unique fingerprint of the                 material. Because the cost of pure ITEs is large, and                 the analytical chemistry is not widely available, there                 is a significant barrier to engineering a fraudulent                 sample to reproduce the native ITE fingerprint of a                 mineral soil amendment. Thus, it would be challenging                 for a stakeholder in a carbon exchange transaction to                 generate a result that produces the anticipated result                 (a high or low amount of carbon removal) while also                 matching the ITE fingerprint generated by a bona fide                 sample. This is a contrast with measurement schemes for                 soil organic carbon, in which the landowner or other                 interested party has an information advantage in terms                 of where or when to sample, which could be used to                 achieve a particular carbon measurement objective (high                 or low).             -   e. Verification Methodology 2 (VM2) has advantages over                 Verification Methodology 1 (VM1) in that it avoids the                 need for the use of a device, which avoids altering the                 soil hydrology or physical environment in a way that                 would impact the observed elemental analysis.             -   f. VM2 may have an advantage over VM1 in not requiring                 tracking of a specific location for recovering the                 sampling column.             -   g. VM2 does, however, include measurement techniques                 that are less widely available; requires specialized                 instruments and personnel; requires additional boundary                 conditions to compute carbon flux (e.g., pre-application                 soil and rock elemental analysis); and employs                 assumptions as to the relationship between cation flux                 and carbon flux.             -   h. Like VM1, VM2 uses the total amount of mineral                 applied and the field area, which could be measured, for                 example, using a digital as-applied map commonly                 accompanying crops input machinery, or truck weights                 before and after mineral delivery. This will be referred                 to as the nominal application rate (AR_(nominal)).             -   i. There are four main calculations in VM2. To the                 extent any one of these factors is known unambiguously                 from other sources, each step in VM2 could be used in                 isolation from the others:                 -   i. Classify, using ITE fingerprinting, whether a                     soil has had a specific mineral applied, which may                     be asserted by an entity wishing to make a claim;                 -   ii. Calculate, using ITE fingerprinting, what the                     actual mineral application rate (AR_(actual)) for a                     specific soil sample was, which will necessarily                     differ in a systematic or random way from the                     average rate for the entire field;                 -   iii. Calculate the amount of divalent cations                     remaining in a control volume relative to the amount                     predicted by the application rate in (ii) above;                 -   iv. Calculate, using the fraction computed in (iii)                     and the mineral potential (Equation 1) computed for                     the feedstock identified in (i) above, the amount of                     carbon dioxide removed.             -   j. In one non-limiting embodiment, the verification                 methodology to classify whether the claimed mineral                 applied is the actual mineral applied is as follows:                 -   i. Collect a sample from mineral to be applied,                     place in a secure vessel and seal with another                     secondary bag in order to reach air-tight                     containment. Label as Mineral Amendment.                 -   ii. Prior to mineral application, collect a 20 g                     sample from cultivated zone of soil (typically at                     around 30 cm, such as in a range of 0 cm to 30 cm),                     place in a secure vessel and seal with another                     secondary bag in order to reach air-tight                     containment. Label as Soil A.                 -   iii. Subsequent to mineral application, collect a 20                     g sample the same control zone as soil A, and store                     under similar conditions. Label as Soil B. Soil B                     could be sampled immediately after mineral                     application or at a later time (e.g., months to                     years afterwards).                 -   iv. Characterize the elemental composition of                     Mineral Amendment, Soil A, and Soil B. Example                     approaches to characterizing the elemental                     composition are described in (v) and (vi).                 -   v. One approach to measuring the elemental                     composition is as follows:                 -    1. In a laboratory setting, unseal the soil samples                     and place 10 grams of Soil A and Soil B in two                     separate beakers.                 -    2. Dissolve the solids in strong acid. For example,                     add 21 mL of strong 1.0 M hydrochloric acid and 7 mL                     of strong 1.0 M nitric acid (total 28 mL acid) to                     each beaker of sterilized soil and stir rigorously                     until solids are dissolved.                 -    3. Filter the sample-containing beakers first                     through a 1- to 5-micron water filter cartridge                     followed by an attached 10 to 20 cm column cation                     exchange resin at a sufficiently slow flow rate of,                     for example, 1 to 5 mL/min. This combination of a                     water filter with a cation exchange column has been                     engineered for optimal performance with soils under                     consideration. Specifically, the 5-micron water                     filter cartridge separates out any larger particles,                     allowing for the smaller particles to exchange its                     bound metals with the subsequent cation exchange                     resin.                 -    4. Flush copious amounts (e.g., 100-200 mL) of 0.5                     to 1.0 M chelator such as, for example,                     ethylenediaminetetraacetic acid (EDTA) at 1-5 mL/min                     through the used filters into their respective                     filtrates. This may collect any additional metals                     that were still adhered to the filters.                 -    5. Send filtrate A (resultant sample from Soil A)                     and filtrate B (resultant sample from Soil B) to an                     analytical laboratory for analysis on an inductively                     coupled plasma mass spectrometer (ICP-MS).                     Measurements may include concentrations of high ppb                     detection of REEs, high ppm detection of Mg, and                     percent mineralogical fractions of SiO2, Al2O3, and                     Fe2O3.                 -    6. The ICP-MS may be set to detect magnesium                     concentrations and the following 17 elements on a                     high ppb or low ppm detection level: Yttrium,                     Scandium, Lanthanum, Cerium, Praseodymium,                     Neodymium, Promethium, Samarium, Europium,                     Gadolinium, Terbium, Dysprosium, Holmium, Erbium,                     Thulium, Ytterbium, Lutetium. Classify light rare                     earth elements (LREEs) as yttrium, scandium,                     lanthanum, cerium, praseodymium, neodymium,                     promethium, and samarium. Classify heavy rare earth                     elements (HREEs) as europium, gadolinium, terbium,                     dysprosium, holmium, erbium, thulium, ytterbium, and                     lutetium. Send an isolated rock material sample for                     ICP-MS analysis. Similar to the filtrate analyses,                     measurements may include concentrations of high ppb                     detection of REEs, high ppm detection of Mg, and                     percent mineralogical fractions of SiO2, Al2O3, and                     Fe2O3.                 -   vi. Another approach to measuring the elemental                     composition is as follows:                 -    1. Calibrate a portable XRF instrument for                     particularly low detection limit of ITEs using a                     calibration standard (such as Bruker proprietary Geo                     calibration+custom ITE standards).                 -    2. Use the portable XRF instrument to analyze the                     Rock Material and Soil A for ITEs (as identified in                     Verification methodology 2), reporting the                     instrumental error (2 standard deviations) as well.                 -    3. Use the portable XRF instrument to analyze Soil                     B for ITEs, reporting the instrumental error (2                     standard deviations) as well.                 -   vii. Once the above elemental composition has been                     determined, calculate the difference for every                     element between Mineral Amendment and Soil A,                     resulting in a vector of differences v_(rock).                     Likewise, compute the difference for every element                     between Soil B and Soil A, resulting in a vector of                     differences v_(soil). To improve performance, each                     element may be divided by an individual factor, such                     as the detection threshold, or the instrumental                     uncertainty, or the elemental composition of a                     reference material. Another means to improve                     performance would be to sum a subset of the elements                     or several distinct subsets of elements before                     computing v_(rock) and v_(soil). Another means to                     improve performance would be to compute indices of                     these summed subsets of elements, for example the                     ratio of the light REEs to the heavy REEs, before                     computing v_(rock) and v_(soil).                 -   viii. Compute the dot product of v_(rock) and                     v_(soil). If the value of this dot product is close                     to 1 (e.g., within a threshold value), then the Soil                     B is positively classified as having the Mineral                     Amendment. If the value of the dot product is less                     than 1 minus a threshold value, then Soil B is                     negatively classified as not having the Mineral                     Amendment.                 -   ix. The threshold value may be determined using a                     variety of means, for example the half-angle between                     the dot product of v_(rock) and v_(soil) and any                     other known v_(rock) and v_(soil); or using a Monte                     Carlo simulation of v_(rock) and v_(soil) that                     accounts for known sources of uncertainty including                     instrumental error, variation in rock elemental                     analysis, or variation of soil elemental analysis.             -   k. In one non-limiting embodiment, the verification                 methodology to calculate the actual mineral application                 rate (AR_(actual)) for a specific soil sample is as                 follows:                 -   i. Characterize the elemental composition the                     elemental composition of Mineral Amendment, Soil A,                     and Soil B as above. Note that there could be                     different analytical chemistry employed if, for                     example, rapid and inexpensive XRF analysis was used                     for classification soon after application, and                     slower and more costly ICP analysis may be used to                     estimate application rates.                 -   ii. Compute the differences in elemental composition                     as above, potentially including similar performance                     enhancements such as normalizing by factors specific                     to each element, summing across subsets of elements,                     and computing indices such as the ratio of light                     REEs to heavy REEs. Such transformed and summed                     variables for a sample will be referred to                     generically as ΣITE_(sample).                 -   iii. The actual application rate of the sample can                     be calculated using the following expression:

$\begin{matrix} {{ARactual} = {x\left\lbrack \frac{\left( {{\sum{ITEs}_{{soil}B}} - {\sum{ITEs}_{{soil}A}}} \right)}{\left( {\sum{ITEs}_{mineral}} \right)} \right\rbrack}} & \left( {{Equation}2} \right) \end{matrix}$

-   -   -   -   l. In one non-limiting embodiment, the verification                 methodology to calculate the amount of divalent cations                 remaining in a control volume relative to the amount                 predicted by the actual mineral application rate                 (AR_(actual)) as follows:                 -   i. The amount of divalent cations applied                     (DCapplied) can be calculated by the proven identity                     of the mineral additive and the actual application                     rate:

DCapplied=ARactual*[Mgmineral+Ca_(mineral)]  (Equation 3)

-   -   -   -   -    where divalent cations are generally restricted in                     this context to Mg and Ca, and Mg_(mineral) and                     Ca_(mineral) is the fractional composition of the                     mineral additive.                 -   ii. The amount of divalent cations remaining                     (DCremain) in the soil could be estimated using the                     same elemental analysis as previously (if, for                     example, ICP-MS was used), or determined from the                     same sample using a different analysis (if, for                     example XRF was used and Mg was not measured).                 -   iii. The fractional progress of carbon dioxide                     removal (CDR) can be estimated by the ratio of                     remaining divalent cations to applied divalent                     cations:

$\begin{matrix} {f_{CDR} = \frac{DCremain}{DCapplied}} & \left( {{Equation}4} \right) \end{matrix}$

-   -   -   -   m. In one non-limiting embodiment, the verification                 methodology to calculate the amount of carbon dioxide                 removed from the control volume is as follows:                 -   i. Assembling MP, f_(CDR), AR_(nominal) and the land                     area applied, the total carbon dioxide removal is:

CDR=f_(CDR)*MP*ARnominal*Area  (Equation 5)

-   -   -   -   n. While Verification Methodology 2 presented herein                 provides a broad framework for the detection and                 application of soil-bound ITEs to estimate long-term                 geologic carbon drawdown, the efficacy of the approach                 can also be improved through the focus on specific                 subsets of ITEs. Non-limiting embodiments of such                 improvements are listed below:                 -   i. The ITEs specified in equation 2, e.g.,                     (ΣITEs_(soil B)), may in fact be represented not by                     the full summation of 17 REEs but instead by the use                     of only LREEs or the use of only HREEs, as defined                     in clause xii. Such a calculation would mean the sum                     of only LREEs in the calculation (yttrium, scandium,                     lanthanum, cerium, praseodymium, neodymium,                     promethium, and samarium) or the sum of only HREEs                     in the calculation (europium, gadolinium, terbium,                     dysprosium, holmium, erbium, thulium, ytterbium, and                     lutetium).                 -   ii. Within the use of only LREEs for the calculation                     (yttrium, scandium, lanthanum, cerium, praseodymium,                     neodymium, promethium, and samarium), some LREEs may                     serve as immobile elements more effectively than                     others. In order to establish an acceptable average                     and standard deviation for the C drawdown                     calculation, a subset of the individual LREEs are                     selected. For example, the subset may include three                     LREEs. The calculation (equation 2) is conducted for                     each of the 3 LREEs individually, and an average and                     standard deviation is then reported for the CDR                     calculation. Among the 3 LREEs, the following                     triplicates are listed as potential, non-limiting                     candidates of interest: [yttrium, scandium,                     lanthanum], [cerium, lanthanum, neodymium], [cerium,                     neodymium, samarium], [yttrium, cerium, neodymium],                     [scandium, neodymium, samarium].                 -   iii. Within the use of only HREEs for the                     calculation (europium, gadolinium, terbium,                     dysprosium, holmium, erbium, thulium, ytterbium, and                     lutetium), some HREEs may serve as immobile elements                     more effectively than others. In order to establish                     an acceptable average and standard deviation for the                     C drawdown calculation, a subset of the individual                     HREEs are selected. For example, the subset may                     include three HREEs. The calculation (equation 2a)                     is conducted for each of the 3 HREEs individually,                     and an average and standard deviation is then                     reported for the CDR calculation. Among the 3 HREEs,                     the following triplicates are listed as potential,                     non-limiting candidates of interest: [europium,                     gadolinium, terbium], [europium, terbium,                     dysprosium], [dysprosium, erbium, ytterbium],                     [europium, erbium, ytterbium], [europium,                     dysprosium, erbium].                 -   iv. In order to establish an acceptable average and                     standard deviation for the C drawdown calculation, a                     subset of the individual REEs are selected. For                     example, the subset may include three REEs Chart 1                     represents a non-limiting list of REE triplicates                     that may enhance the efficacy of this C drawdown                     calculation.

Chart 1. A Non-Limiting List of 455 REE Triplicates that can be Used to Effectively Triangulate a C Drawdown Estimation

(‘Y’, ‘La’, ‘Ce’), (‘Y’, ‘La’, ‘Pr’), (‘Y’, ‘La’, ‘Nd’), (‘Y’, ‘La’, ‘Sm’), (‘Y’, ‘La’, ‘Eu’), (‘Y’, ‘La’, ‘Gd’), (‘Y’, ‘La’, ‘Tb’), (‘Y’, ‘La’, ‘Dy’), (‘Y’, ‘La’, ‘Ho’), (‘Y’, ‘La’, ‘Er’), (‘Y’, ‘La’, ‘Tm’), (‘Y’, ‘La’, ‘Yb’), (‘Y’, ‘La’, ‘Lu’), (‘Y’, ‘Ce’, ‘Pr’), (‘Y’, ‘Ce’, ‘Nd’), (‘Y’, ‘Ce’, ‘Sm’), (‘Y’, ‘Ce’, ‘Eu’), (‘Y’, ‘Ce’, ‘Gd’), (‘Y’, ‘Ce’, ‘Tb’), (‘Y’, ‘Ce’, ‘Dy’), (‘Y’, ‘Ce’, ‘Ho’), (‘Y’, ‘Ce’, ‘Er’), (‘Y’, ‘Ce’, ‘Tm’), (‘Y’, ‘Ce’, ‘Yb’), (‘Y’, ‘Ce’, ‘Lu’), (‘Y’, ‘Pr’, ‘Nd’), (‘Y’, ‘Pr’, ‘Sm’), (‘Y’, ‘Pr’, ‘Eu’), (‘Y’, ‘Pr’, ‘Gd’), (‘Y’, ‘Pr’, ‘Tb’), (‘Y’, ‘Pr’, ‘Dy’), (‘Nd’, ‘Pr’, ‘Ho’), (‘Y’, ‘Pr’, ‘Er’), (‘Y’, ‘Pr’, ‘Tm’), (‘Y’, ‘Pr’, ‘Yb’), (‘Y’, ‘Pr’, ‘Lu’), (‘Y’, ‘Nd’, ‘Sm’), (‘Y’, ‘Nd’, ‘Eu’), (‘Y’, ‘Nd’, ‘Gd’), (‘Y’, ‘Nd’, ‘Tb’), (‘Y’, ‘Nd’, ‘Dy’), (‘Y’, ‘Nd’, ‘Ho’), (‘Y’, ‘Nd’, ‘Er’), (‘Y’, ‘Nd’, ‘Tm’), (‘Y’, ‘Nd’, ‘Yb’), (‘Y’, ‘Nd’, ‘Lu’), (‘Y’, ‘Sm’, ‘Eu’), (‘Y’, ‘Sm’, ‘Gd’), (‘Y’, ‘Sm’, ‘Tb’), (‘Y’, ‘Sm’, ‘Dy’), (‘Y’, ‘Sm’, ‘Ho’), (‘Y’, ‘Sm’, ‘Er’), (‘Y’, ‘Sm’, ‘Tm’), (‘Y’, ‘Sm’, ‘Yb’), (‘Y’, ‘Sm’, ‘Lu’), (‘Y’, ‘Eu’, ‘Gd’), (‘Y’, ‘Eu’, ‘Tb’), (‘Y’, ‘Eu’, ‘Dy’), (‘Y’, ‘Eu’, ‘Ho’), (‘Y’, ‘Eu’, ‘Er’), (‘Y’, ‘Eu’, ‘Tm’), (‘Y’, ‘Eu’, ‘Yb’), (‘Y’, ‘Eu’, ‘Lu’), (‘Y’, ‘Gd’, ‘Tb’), (‘Y’, ‘Gd’, ‘Dy’), (‘Y’, ‘Gd’, ‘Ho’), (‘Y’, ‘Gd’, ‘Er’), (‘Y’, ‘Gd’, ‘Tm’), (‘Y’, ‘Gd’, ‘Yb’), (‘Y’, ‘Gd’, ‘Lu’), (‘Y’, ‘Tb’, ‘Dy’), (‘Y’, ‘Tb’, ‘Ho’), (‘Y’, ‘Tb’, ‘Er’), (‘Y’, ‘Tb’, ‘Tm’), (‘Y’, ‘Tb’, ‘Yb’), (‘Y’, ‘Tb’, ‘Lu’), (‘Y’, ‘Dy’, ‘Ho’), (‘Y’, ‘Dy’, ‘Er’), (‘Y’, ‘Dy’, ‘Tm’), (‘Y’, Dy′, ‘Yb’), (‘Y’, ‘Dy’, ‘Lu’), (‘Y’, ‘Ho’, Er′), (‘Y’, ‘Ho’, ‘Tm’), (‘Y’, ‘Ho’, ‘Yb’), (‘Y’, ‘Ho’, ‘Lu’), (‘Y’, ‘Er’, ‘Tm’), (‘Y’, ‘Er’, ‘Yb’), (‘Y’, ‘Er’, ‘Lu’), (‘Y’, ‘Tm’, ‘Yb’), (‘Y’, ‘Tm’, ‘Lu’), (‘Y’, ‘Yb’, ‘Lu’), (‘La’, ‘Ce’, ‘Pr’), (‘La’, ‘Ce’, ‘Nd’), (‘La’, ‘Ce’, ‘Sm’), (‘La’, ‘Ce’, ‘Eu’), (‘La’, ‘Ce’, ‘Gd’), (‘La’, ‘Ce’, ‘Tb’), (‘La’, ‘Ce’, ‘Dy’), (‘La’, ‘Ce’, ‘Ho’), (‘La’, ‘Ce’, ‘Er’), (‘La’, ‘Ce’, ‘Tm’), (‘La’, ‘Ce’, ‘Yb’), (‘La’, ‘Ce’, ‘Lu’), (‘La’, ‘Pr’, ‘Nd’), (‘La’, ‘Pr’, ‘Sm’), (‘La’, ‘Pr’, ‘Eu’), (‘La’, ‘Pr’, ‘Gd’), (‘La’, ‘Pr’, ‘Tb’), (‘La’, ‘Pr’, ‘Dy’), (‘La’, ‘Pr’, ‘Ho’), (‘La’, ‘Pr’, ‘Er’), (‘La’, ‘Pr’, ‘Tm’), (‘La’, ‘Pr’, ‘Yb’), (‘La’, ‘Pr’, ‘Lu’), (‘La’, ‘Nd’, ‘Sm’), (‘La’, ‘Nd’, ‘Eu’), (‘La’, ‘Nd’, ‘Gd’), (‘La’, ‘Nd’, ‘Tb’), (‘La’, ‘Nd’, ‘Dy’), (‘La’, ‘Nd’, ‘Ho’), (‘La’, ‘Nd’, ‘Er’), (‘La’, ‘Nd’, ‘Tm’), (‘La’, ‘Nd’, ‘Yb’), (‘La’, ‘Nd’, ‘Lu’), (‘La’, ‘Sm’, ‘Eu’), (‘La’, ‘Sm’, ‘Gd’), (‘La’, ‘Sm’, ‘Tb’), (‘La’, ‘Sm’, ‘Dy’), (‘La’, ‘Sm’, ‘Ho’), (‘La’, ‘Sm’, ‘Er’), (‘La’, ‘Sm’, ‘Tm’), (‘La’, ‘Sm’, ‘Yb’), (‘La’, ‘Sm’, ‘Lu’), (‘La’, ‘Eu’, ‘Gd’), (‘La’, ‘Eu’, ‘Tb’), (‘La’, ‘Eu’, ‘Dy’), (‘La’, ‘Eu’, ‘Ho’), (‘La’, ‘Eu’, ‘Er’), (‘La’, ‘Eu’, ‘Tm’), (‘La’, ‘Eu’, ‘Yb’), (‘La’, ‘Eu’, ‘Lu’), (‘La’, ‘Gd’, ‘Tb’), (‘La’, ‘Gd’, ‘Dy’), (‘La’, ‘Gd’, ‘Ho’), (‘La’, ‘Gd’, ‘Er’), (‘La’, ‘Gd’, ‘Tm’), (‘La’, ‘Gd’, ‘Yb’), (‘La’, ‘Gd’, ‘Lu’), (‘La’, ‘Tb’, ‘Dy’), (‘La’, ‘Tb’, ‘Ho’), (‘La’, ‘Tb’, ‘Er’), (‘La’, ‘Tb’, ‘Tm’), (‘La’, ‘Tb’, ‘Yb’), (‘La’, ‘Tb’, ‘Lu’), (‘La’, ‘Dy’, ‘Ho’), (‘La’, ‘Dy’, ‘Er’), (‘La’, ‘Dy’, ‘Tm’), (‘La’, ‘Dy’, ‘Yb’), (‘La’, ‘Dy’, ‘Lu’), (‘La’, ‘Ho’, ‘Er’), (‘La’, ‘Ho’, ‘Tm’), (‘La’, ‘Ho’, ‘Yb’), (‘La’, ‘Ho’, ‘Lu’), (‘La’, ‘Er’, ‘Tm’), (‘La’, ‘Er’, ‘Yb’), (‘La’, ‘Er’, ‘Lu’), (‘La’, ‘Tm’, ‘Yb’), (‘La’, ‘Tm’, ‘Lu’), (‘La’, ‘Yb’, ‘Lu’), (‘Ce’, ‘Pr’, ‘Nd’), (‘Ce’, ‘Pr’, ‘Sm’), (‘Ce’, ‘Pr’, ‘Eu’), (‘Ce’, ‘Pr’, ‘Gd’), (‘Ce’, ‘Pr’, ‘Tb’), (‘Ce’, ‘Pr’, ‘Dy’), (‘Ce’, ‘Pr’, ‘Ho’), (‘Ce’, ‘Pr’, ‘Er’), (‘Ce’, ‘Pr’, ‘Tm’), (‘Ce’, ‘Pr’, ‘Yb’), (‘Ce’, ‘Pr’, ‘Lu’), (‘Ce’, ‘Nd’, ‘Sm’), (‘Ce’, ‘Nd’, ‘Eu’), (‘Ce’, ‘Nd’, ‘Gd’), (‘Ce’, ‘Nd’, ‘Tb’), (‘Ce’, ‘Nd’, ‘Dy’), (‘Ce’, ‘Nd’, ‘Ho’), (‘Ce’, ‘Nd’, ‘Er’), (‘Ce’, ‘Nd’, ‘Tm’), (‘Ce’, ‘Nd’, ‘Yb’), (‘Ce’, ‘Nd’, ‘Lu’), (‘Ce’, ‘Sm’, ‘Eu’), (‘Ce’, ‘Sm’, ‘Gd’), (‘Ce’, ‘Sm’, ‘Tb’), (‘Ce’, ‘Sm’, ‘Dy’), (‘Ce’, ‘Sm’, ‘Ho’), (‘Ce’, ‘Sm’, ‘Er’), (‘Ce’, ‘Sm’, ‘Tm’), (‘Ce’, ‘Sm’, ‘Yb’), (‘Ce’, ‘Sm’, ‘Lu’), (‘Ce’, ‘Eu’, ‘Gd’), (‘Ce’, ‘Eu’, ‘Tb’), (‘Ce’, ‘Eu’, ‘Dy’), (‘Ce’, ‘Eu’, ‘Ho’), (‘Ce’, ‘Eu’, ‘Er’), (‘Ce’, ‘Eu’, ‘Tm’), (‘Ce’, ‘Eu’, ‘Yb’), (‘Ce’, ‘Eu’, ‘Lu’), (‘Ce’, ‘Gd’, ‘Tb’), (‘Ce’, ‘Gd’, ‘Dy’), (‘Ce’, ‘Gd’, ‘Ho’), (‘Ce’, ‘Gd’, ‘Er’), (‘Ce’, ‘Gd’, ‘Tm’), (‘Ce’, ‘Gd’, ‘Yb’), (‘Ce’, ‘Gd’, ‘Lu’), (‘Ce’, ‘Tb’, ‘Dy’), (‘Ce’, ‘Tb’, ‘Ho’), (‘Ce’, ‘Tb’, ‘Er’), (‘Ce’, ‘Tb’, ‘Tm’), (‘Ce’, ‘Tb’, ‘Yb’), (‘Ce’, ‘Tb’, ‘Lu’), (‘Ce’, ‘Dy’, ‘Ho’), (‘Ce’, ‘Dy’, ‘Er’), (‘Ce’, ‘Dy’, ‘Tm’), (‘Ce’, ‘Dy’, ‘Yb’), (‘Ce’, ‘Dy’, ‘Lu’), (‘Ce’, ‘Ho’, ‘Er’), (‘Ce’, ‘Ho’, ‘Tm’), (‘Ce’, ‘Ho’, ‘Yb’), (‘Ce’, ‘Ho’, ‘Lu’), (‘Ce’, ‘Er’, ‘Tm’), (‘Ce’, ‘Er’, ‘Yb’), (‘Ce’, ‘Er’, ‘Lu’), (‘Ce’, ‘Tm’, ‘Yb’), (‘Ce’, ‘Tm’, ‘Lu’), (‘Ce’, ‘Yb’, ‘Lu’), (‘Pr’, ‘Nd’, ‘Sm’), (‘Pr’, ‘Nd’, ‘Eu’), (‘Pr’, ‘Nd’, ‘Gd’), (‘Pr’, ‘Nd’, ‘Tb’), (‘Pr’, ‘Nd’, ‘Dy’), (‘Pr’, ‘Nd’, ‘Ho’), (‘Pr’, ‘Nd’, ‘Er’), (‘Pr’, ‘Nd’, ‘Tm’), (‘Pr’, ‘Nd’, ‘Yb’), (‘Pr’, ‘Nd’, ‘Lu’), (‘Pr’, ‘Sm’, ‘Eu’), (‘Pr’, ‘Sm’, ‘Gd’), (‘Pr’, ‘Sm’, ‘Tb’), (‘Pr’, ‘Sm’, ‘Dy’), (‘Pr’, ‘Sm’, ‘Ho’), (‘Pr’, ‘Sm’, ‘Er’), (‘Pr’, ‘Sm’, ‘Tm’), (‘Pr’, ‘Sm’, ‘Yb’), (‘Pr’, ‘Sm’, ‘Lu’), (‘Pr’, ‘Eu’, ‘Gd’), (‘Pr’, ‘Eu’, ‘Tb’), (‘Pr’, ‘Eu’, ‘Dy’), (‘Pr’, ‘Eu’, ‘Ho’), (‘Pr’, ‘Eu’, ‘Er’), (‘Pr’, ‘Eu’, ‘Tm’), (‘Pr’, ‘Eu’, ‘Yb’), (‘Pr’, ‘Eu’, ‘Lu’), (‘Pr’, ‘Gd’, ‘Tb’), (‘Pr’, ‘Gd’, ‘Dy’), (‘Pr’, ‘Gd’, ‘Ho’), (‘Pr’, ‘Gd’, ‘Er’), (‘Pr’, ‘Gd’, ‘Tm’), (‘Pr’, ‘Gd’, ‘Yb’), (‘Pr’, ‘Gd’, ‘Lu’), (‘Pr’, ‘Tb’, ‘Dy’), (‘Pr’, ‘Tb’, ‘Ho’), (‘Pr’, ‘Tb’, ‘Er’), (‘Pr’, ‘Tb’, ‘Tm’), (‘Pr’, ‘Tb’, ‘Yb’), (‘Pr’, ‘Tb’, ‘Lu’), (‘Pr’, ‘Dy’, ‘Ho’), (‘Pr’, ‘Dy’, ‘Er’), (‘Pr’, ‘Dy’, ‘Tm’), (‘Pr’, ‘Dy’, ‘Yb’), (‘Pr’, ‘Dy’, ‘Lu’), (‘Pr’, ‘Ho’, ‘Er’), (‘Pr’, ‘Ho’, ‘Tm’), (‘Pr’, ‘Ho’, ‘Yb’), (‘Pr’, ‘Ho’, ‘Lu’), (‘Pr’, ‘Er’, ‘Tm’), (‘Pr’, ‘Er’, ‘Yb’), (‘Pr’, ‘Er’, ‘Lu’), (‘Pr’, ‘Tm’, ‘Yb’), (‘Pr’, ‘Tm’, ‘Lu’), (‘Pr’, ‘Yb’, ‘Lu’), (‘Nd’, ‘Sm’, ‘Eu’), (‘Nd’, ‘Sm’, ‘Gd’), (‘Nd’, ‘Sm’, ‘Tb’), (‘Nd’, ‘Sm’, ‘Dy’), (‘Nd’, ‘Sm’, ‘Ho’), (‘Nd’, ‘Sm’, ‘Er’), (‘Nd’, ‘Sm’, ‘Tm’), (‘Nd’, ‘Sm’, ‘Yb’), (‘Nd’, ‘Sm’, ‘Lu’), (‘Nd’, ‘Eu’, ‘Gd’), (‘Nd’, ‘Eu’, ‘Tb’), (‘Nd’, ‘Eu’, ‘Dy’), (‘Nd’, ‘Eu’, ‘Ho’), (‘Nd’, ‘Eu’, ‘Er’), (‘Nd’, ‘Eu’, ‘Tm’), (‘Nd’, ‘Eu’, ‘Yb’), (‘Nd’, ‘Eu’, ‘Lu’), (‘Nd’, ‘Gd’, ‘Tb’), (‘Nd’, ‘Gd’, ‘Dy’), (‘Nd’, ‘Gd’, ‘Ho’), (‘Nd’, ‘Gd’, ‘Er’), (‘Nd’, ‘Gd’, ‘Tm’), (‘Nd’, ‘Gd’, ‘Yb’), (‘Nd’, ‘Gd’, ‘Lu’), (‘Nd’, ‘Tb’, ‘Dy’), (‘Nd’, ‘Tb’, ‘Ho’), (‘Nd’, ‘Tb’, ‘Er’), (‘Nd’, ‘Tb’, ‘Tm’), (‘Nd’, ‘Tb’, ‘Yb’), (‘Nd’, ‘Tb’, ‘Lu’), (‘Nd’, ‘Dy’, ‘Ho’), (‘Nd’, ‘Dy’, ‘Er’), (‘Nd’, ‘Dy’, ‘Tm’), (‘Nd’, ‘Dy’, ‘Yb’), (‘Nd’, ‘Dy’, ‘Lu’), (‘Nd’, ‘Ho’, ‘Er’), (‘Nd’, ‘Ho’, ‘Tm’), (‘Nd’, ‘Ho’, ‘Yb’), (‘Nd’, ‘Ho’, ‘Lu’), (‘Nd’, ‘Er’, ‘Tm’), (‘Nd’, ‘Er’, ‘Yb’), (‘Nd’, ‘Er’, ‘Lu’), (‘Nd’, ‘Tm’, ‘Yb’), (‘Nd’, ‘Tm’, ‘Lu’), (‘Nd’, ‘Yb’, ‘Lu’), (‘Sm’, ‘Eu’, ‘Gd’), (‘Sm’, ‘Eu’, ‘Tb’), (‘Sm’, ‘Eu’, ‘Dy’), (‘Sm’, ‘Eu’, ‘Ho’), (‘Sm’, ‘Eu’, ‘Er’), (‘Sm’, ‘Eu’, ‘Tm’), (‘Sm’, ‘Eu’, ‘Yb’), (‘Sm’, ‘Eu’, ‘Lu’), (‘Sm’, ‘Gd’, ‘Tb’), (‘Sm’, ‘Gd’, ‘Dy’), (‘Sm’, ‘Gd’, ‘Ho’), (‘Sm’, ‘Gd’, ‘Er’), (‘Sm’, ‘Gd’, ‘Tm’), (‘Sm’, ‘Gd’, ‘Yb’), (‘Sm’, ‘Gd’, ‘Lu’), (‘Sm’, ‘Tb’, ‘Dy’), (‘Sm’, ‘Tb’, ‘Ho’), (‘Sm’, ‘Tb’, ‘Er’), (‘Sm’, ‘Tb’, ‘Tm’), (‘Sm’, ‘Tb’, ‘Yb’), (‘Sm’, ‘Tb’, ‘Lu’), (‘Sm’, ‘Dy’, ‘Ho’), (‘Sm’, ‘Dy’, ‘Er’), (‘Sm’, ‘Dy’, ‘Tm’), (‘Sm’, ‘Dy’, ‘Yb’), (‘Sm’, ‘Dy’, ‘Lu’), (‘Sm’, ‘Ho’, ‘Er’), (‘Sm’, ‘Ho’, ‘Tm’), (‘Sm’, ‘Ho’, ‘Yb’), (‘Sm’, ‘Ho’, ‘Lu’), (‘Sm’, ‘Er’, ‘Tm’), (‘Sm’, ‘Er’, ‘Yb’), (‘Sm’, ‘Er’, ‘Lu’), (‘Sm’, ‘Tm’, ‘Yb’), (‘Sm’, ‘Tm’, ‘Lu’), (‘Sm’, ‘Yb’, ‘Lu’), (‘Eu’, ‘Gd’, ‘Tb’), (‘Eu’, ‘Gd’, ‘Dy’), (‘Eu’, ‘Gd’, ‘Ho’), (‘Eu’, ‘Gd’, ‘Er’), (‘Eu’, ‘Gd’, ‘Tm’), (‘Eu’, ‘Gd’, ‘Yb’), (‘Eu’, ‘Gd’, ‘Lu’), (‘Eu’, ‘Tb’, ‘Dy’), (‘Eu’, ‘Tb’, ‘Ho’), (‘Eu’, ‘Tb’, ‘Er’), (‘Eu’, ‘Tb’, ‘Tm’), (‘Eu’, ‘Tb’, ‘Yb’), (‘Eu’, ‘Tb’, ‘Lu’), (‘Eu’, ‘Dy’, ‘Ho’), (‘Eu’, ‘Dy’, ‘Er’), (‘Eu’, ‘Dy’, ‘Tm’), (‘Eu’, ‘Dy’, ‘Yb’), (‘Eu’, ‘Dy’, ‘Lu’), (‘Eu’, ‘Ho’, ‘Er’), (‘Eu’, ‘Ho’, ‘Tm’), (‘Eu’, ‘Ho’, ‘Yb’), (‘Eu’, ‘Ho’, ‘Lu’), (‘Eu’, ‘Er’, ‘Tm’), (‘Eu’, ‘Er’, ‘Yb’), (‘Eu’, ‘Er’, ‘Lu’), (‘Eu’, ‘Tm’, ‘Yb’), (‘Eu’, ‘Tm’, ‘Lu’), (‘Eu’, ‘Yb’, ‘Lu’), (‘Gd’, ‘Tb’, ‘Dy’), (‘Gd’, ‘Tb’, ‘Ho’), (‘Gd’, ‘Tb’, ‘Er’), (‘Gd’, ‘Tb’, ‘Tm’), (‘Gd’, ‘Tb’, ‘Yb’), (‘Gd’, ‘Tb’, ‘Lu’), (‘Gd’, ‘Dy’, ‘Ho’), (‘Gd’, ‘Dy’, ‘Er’), (‘Gd’, ‘Dy’, ‘Tm’), (‘Gd’, ‘Dy’, ‘Yb’), (‘Gd’, ‘Dy’, ‘Lu’), (‘Gd’, ‘Ho’, ‘Er’), (‘Gd’, ‘Ho’, ‘Tm’), (‘Gd’, ‘Ho’, ‘Yb’), (‘Gd’, ‘Ho’, ‘Lu’), (‘Gd’, ‘Er’, ‘Tm’), (‘Gd’, ‘Er’, ‘Yb’), (‘Gd’, ‘Er’, ‘Lu’), (‘Gd’, ‘Tm’, ‘Yb’), (‘Gd’, ‘Tm’, ‘Lu’), (‘Gd’, ‘Yb’, ‘Lu’), (‘Tb’, ‘Dy’, ‘Ho’), (‘Tb’, ‘Dy’, ‘Er’), (‘Tb’, ‘Dy’, ‘Tm’), (‘Tb’, ‘Dy’, ‘Yb’), (‘Tb’, ‘Dy’, ‘Lu’), (‘Tb’, ‘Ho’, ‘Er’), (‘Tb’, ‘Ho’, ‘Tm’), (‘Tb’, ‘Ho’, ‘Yb’), (‘Tb’, ‘Ho’, ‘Lu’), (‘Tb’, ‘Er’, ‘Tm’), (‘Tb’, ‘Er’, ‘Yb’), (‘Tb’, ‘Er’, ‘Lu’), (‘Tb’, ‘Tm’, ‘Yb’), (‘Tb’, ‘Tm’, ‘Lu’), (‘Tb’, ‘Yb’, ‘Lu’), (‘Dy’, ‘Ho’, ‘Er’), (‘Dy’, ‘Ho’, ‘Tm’), (‘Dy’, ‘Ho’, ‘Yb’), (‘Dy’, ‘Ho’, ‘Lu’), (‘Dy’, ‘Er’, ‘Tm’), (‘Dy’, ‘Er’, ‘Yb’), (‘Dy’, ‘Er’, ‘Lu’), (‘Dy’, ‘Tm’, ‘Yb’), (‘Dy’, ‘Tm’, ‘Lu’), (‘Dy’, ‘Yb’, ‘Lu’), (‘Ho’, ‘Er’, ‘Tm’), (‘Ho’, ‘Er’, ‘Yb’), (‘Ho’, ‘Er’, ‘Lu’), (‘Ho’, ‘Tm’, ‘Yb’), (‘Ho’, ‘Tm’, ‘Lu’), (‘Ho’, ‘Yb’, ‘Lu’), (‘Er’, ‘Tm’, ‘Yb’), (‘Er’, ‘Tm’, ‘Lu’), (‘Er’, ‘Yb’, ‘Lu’), (‘Tm’, ‘Yb’, ‘Lu’)

-   -   3. Example Verification methodology 3: this methodology expands         on Verification methodology 2 by the use of naturally occurring         microbial cation exchangers, including bacteria and fungi.         -   i. As above but right before step vii (unsealing samples in             laboratory), add the following steps:         -   ii. Lyse the microbes. For example, autoclave each             sample-containing beaker for steam sterilization at 250° F.             at 15 psi for 15 minutes. This may lyse any microbes and             cause an active release of bio-adsorbed metals.         -   iii. Let sample-containing beakers cool to room temperature             before proceeding.         -   iv. The filter in step (ix) may now act to additionally             remove any larger aggregates of microbial cell suspensions             that did not lyse in the autoclaving process.         -   v. The added EDTA in step (x) in Verification Methodology 2             may act to additionally chelate any REEs that are complexed             to the cell wall or organic molecules of the microbial             genetic material (as a result of cell lysis).         -   vi. In conjunction, verification methodology 3 provides a             protocol to achieve full recovery of REEs that were retained             in the top 10 cm of soil due to the following biogeochemical             processes:             -   1. Mineral surface interface complexation.             -   2. The cation exchange capacity inherent to soils due to                 organic matter.             -   3. Microbially mediated surface biosorption and/or                 active biological absorption pathways including but not                 limited to REE-aqueous complexation with internal                 genetic material of individual microbial cells found in                 natural soils and sediments.     -   B. Example systems and methods to enhance the agronomic         performance and ecosystem co-benefits:         -   In these non-limiting embodiments, product formulations are             detailed that improve the soil quality for improved             agronomic applications as well as embodiments that specify             improvements on crop health and an ability for plants to             protect themselves from pathogens.         -   Addition of macronutrients that enhance the agronomic             benefits of the applied mineral. Example: addition of             elemental 1-5% by weight formulation K or Ca or inexpensive             REE such as La to improve use cases of pulverized Mg₂SiO₄ by             improving the nutrient balance of the soil to match the             needs of actively growing plants. Application rates for K             and Ca may range from 50-100 ppm and lanthanide addition             rates may range from 1-50 ppm.         -   The 1-5% by volume addition of slow-release acidifiers in             the form of elements that maintain the acidity of the soil             despite the tendency of the applied mineral to reduce soil             acidity in the weathering process. Example: addition of             minerals with Al (such as gibbsite, Al(OH)₃) or S (such as             gypsum, CaSO₄)-2H₂O), in a rate of 1-10% by weight of total             formulation, which contribute to maintaining soil acidity,             and thus maintain high rates of weathering, which             counteracts the tendency of forsterite weathering to             increase alkalinity, which slows rates of weathering.         -   The incorporation of additional micronutrients such as zinc             (1-5% by weight compared to mineral amendment) to reduce             ecosystem losses of phosphorus and downstream ecosystem             impacts of phosphate-based fertilizers, such as             eutrophication. Phosphates are immobilized via precipitation             reactions with the additional zinc metal, so zinc addition             slows the transport and reduces mobility of phosphate in the             subsoil. As a consequence, phosphate-based fertilizer             applications can be performed more safely and with higher             confidence that downstream waterways will not form algal             blooms and lead to anoxic, uninhabitable waterways for             aquatic life. The addition of 1-32 tons/hectare of mineral             in conjunction with 1-5% by weight zinc in fields with heavy             phosphate application reduces the likelihood of significant             phosphate leaching. This also increases nutrient use             efficiency, which reduces fertilizer cost to farmers and             reduces negative environmental impacts to society.             Specifically, phosphate-zinc precipitates become             slow-releasing over time due to their immobilization in the             soil as a solid phase. This provides longer timeframes for             plants to access the phosphate application, reducing the             frequency of fertilization.         -   The method of mixing of different mineral adjuvants to the             primary mineral used for carbon removal can be varied, with             impacts on performance. In some embodiments, the admixture             (e.g., of gypsum and forsterite) could be completely             emulsified. In some embodiments, a nutrient, such as urea,             could represent a core that is subsequently coated with a             shell of silicate mineral used for carbon removal. In some             embodiments the silicate mineral could be the core, and the             nutrient, such as urea, could be the coating. In each of             these cases, the embodiment can be optimized so as to reduce             environmental losses of the nutrient, and increase             availability to the plant, while providing the acidity             necessary for the silicate mineral weathering. In some             embodiments, this may represent a “slow release” nutrient             that does not mineralize too quickly and is synchronized             more favorably with plant demand.         -   Comminution, or pulverization, may help reproduce the             expected kinetics of alkalizers such as pulverized limestone             or dolomite, known as aglime. Aglime has well-characterized             kinetics originating in the particle size distribution of             the product, which are in some jurisdictions legally             regulated to meet certain requirements. A representative             cross section of dissolution kinetics based on actual aglime             mesh size observations is depicted in FIG. 2 .         -   It naturally follows that agronomic performance expectations             for silicate minerals used for ERW should follow similar             reaction kinetics, particularly in the first year after             application, while also meeting the goals for CDR. Thus, an             ideal particle size distribution may be tuned to meet this             goal. The following shows the kinetics for a particle size             distribution of a pulverized silicate with median particle             size of 80-100 um, such as 90 um, which closely approximates             the alkalinity release dynamics for aglime.         -   The small particle sizes produced by pulverization as above             are valuable for performance as an aglime substitute and CDR             mechanism, but introduce their own set of potential             challenges. One potential challenge is that small particle             sizes may fall within regulated categories such as PM10 or             PM2.5; another potential challenge is the product may not be             easily transferred from one vessel to another (so-called             “flowability”) because it has a tendency to settle into a             compact mass; the product may also not be applied uniformly             by extant farm equipment; potentially low uniformity             application impacts the agronomic performance as well as the             sampling density needed for carbon removal verification. In             one potential formulation, the product is pelletized after             pulverization, using a common binder such as lignosulfate in             a 3-5% ratio by weight of the total formulation. The amount             of binder may be optimized to improve performance             characteristics during transport and application, but             minimize the water and energy needed to dissolve the pellet             once it is in the field. Pelletizing the product, into a             size range of, for example, 0.5 mm to 3 mm increases the             flowability; reduces the prevalence of dust, including the             risk of asbestos exposure; enables the use of extant crop             input application equipment; and improves the evenness of             field distribution, which has the agronomic and carbon             verification benefits identified. Pelletizing in this size             range also ensures that an adequate number of pellets fall             onto any land area which may subsequently be sampled for             analysis.         -   A desiccated but living biological compound, such as a             mycorrhizal inoculum, may be used to coat the agglomerated             and dried pellets, so as to enhance the dissolution of the             pellet itself after application. This may be distinct from a             fungal adjuvant to the pellet to increase dissolution of the             silicate minerals themselves.         -   To accommodate a range of soil types from acidic to neutral             pH, the product may be differentiated into different             particle size distributions so as to achieve a consistent             rate of weathering across different soil types. For example             a consistent rate of weathering may be that the entire             applied amount of mineral product weathers in 9 months,             allowing a subsequent application every year. To achieve             this, an acidic soil may have pellets that contain particles             with a modal size on the order of 100 um, while a neutral             soil may have pellets that contain particles with a modal             size on the order of 10 um. The negative consequence of             applying a fine particle in an acidic soil may be that it             dissolves too quickly, swinging the pH of the soil too             quickly, and altering the nutrient availability severely in             the growing plant. The negative consequence of applying a             coarse particle in a neutral soil may be that the particle             weathers too slowly or is functionally inert, which does not             remove carbon as intended, and may subject the farmer or the             vendor to risk of clawbacks for payments received for carbon             removal.     -   C. Example systems and methods to control or enhance the         performance as a securitized carbon removal method:         -   In these non-limiting embodiments, product formulations are             described that improve the marketability of pulverized and             optionally pelletized mineral amendments as a verifiable             carbon removal method, irrespective of their impact on             agronomic performance. Such changes in marketability             increase the value of the carbon product, for example for             detecting and preventing fraud, or increase the dissolution             rate (mass per area per year) to accelerate the timing of             reapplication, which raises the value in a discounted cash             flow analysis. The general scheme is depicted in FIG. 4 .         -   The addition of low cost and inert trace elements, for             example 1-5 ppm neodymium or lanthanum, to a mineral             amendment, beyond the natural abundances present in the ore             body, improves performance in Verification methods 2 and 3.             Specifically, the additional elements reduce measurement             uncertainty owing to low natural abundance calculations as             well as uncertainty owing to variability from the source             mineral. Reduction of these uncertainties improves the             detectability of true positives and true negatives. This             principle could be applied to many potential soil amendments             and fertilizers to verify provenance as pertains to legal             contracts.         -   The addition of binders to create aggregations of the ground             mineral that could reduce drift, which improves distribution             uniformity; reduces potential respiratory health impacts;             and/or improves applicability of the applied mineral using             commercially available equipment. For example, a biofilm             mediating organic compound, such as alginate or chitosan,             could be mixed with a pulverized mineral with a particle             size of approximately 100 microns to achieve an aggregated             pellet size of 1 millimeter. This would maintain the             advantages of fine particle size, particularly the high             specific surface area (m²/g) that mediates dissolution rate,             while offsetting potential limitations outlined above. An             example methodology for aggregating ground minerals could             include these steps:             -   Dissolve 10 grams of alginate powder into solution to                 create a 0.5 M-1.0 M alginic acid solution.             -   Heat solution to 80-100° F. to dissolve alginate powder                 fully if necessary.             -   Spray aerosol sized particles of dissolved alginate                 powder onto the ground rock material in order to create                 a biofilm-coated rock material. Apply a consistent spray                 of 100 mL for each 100 gram of rock (1:1 v/w).             -   The resulting aggregates may have increased bulk density                 as well as higher aggregating properties due to van der                 Waals force attraction between the individual rock                 particles.         -   Dissolution rates can be modified by non-living organic             molecules applied concurrently with the mineral amendment.             For example, protonated microbes such as acid-treated             Arthrobacter nicotianae can constitute an initial release of             protons to attack the ground rock materials' crystal             structure. This method of acidification for optimal             accelerated weathering of rock material may occur even             during winter/cold climate. Because biologically mediated             processes can have sharp thresholds, e.g., under freezing             conditions, such a chemically controlled process would             exhibit greater ability to expedite rock breakdown over a             range of environmental conditions. To implement this             methodology, we outline the following steps:             -   1) De-frost an aliquot of A. nicotianae in 5 mL of Luria                 broth for about 24 hours at exactly 30° C.             -   2) Sub-culture into a larger volume of Luria broth at a                 1:50 dilution and allow growth for another 24 hours at                 30° C.             -   3) During growth steps #1 and 2, cultures may be shaken,                 for example at 200-220 RPM, for aeration.             -   4) After culture has been grown for 48 hours in total,                 centrifuge the cell suspension.             -   5) Collect cell pellet and take a small amount and set                 it aside. Weigh wet weight, dry at 60° C. overnight, and                 weigh dry amount to obtain wet:dry conversion.             -   6) Develop an OD₆₀₀ to wet weight to dry weight                 conversion by taking 5 varying amounts of wet aliquots                 of wet biomass and measuring optical density given its                 known wet mass. Wet aliquots may have a mass of about 1,                 4, 8, 12, 16 wet grams and be suspended in 100 mL of DI                 water.             -   7) Wash cells in 0.1 M NaCl solution.                 -   a. Centrifuge cells+growth media at 4000×g.                 -   b. Carefully pour out LB broth.                 -   c. Add 0.1 M NaCl solution.                 -   d. Centrifuge cells+NaCl solution at 4000×g.                 -   e. Carefully pour out NaCl solution.             -   8) Protonate the cells while wet.                 -   a. Re-suspend the wet biomass in an acidic (e.g., pH                     3.0) solution using a dilute hydrochloric acid                     solution (0.001-0.01 M).                 -   b. Centrifuge cells+HCl solution at 4000×g.                 -   c. Carefully pour out solution.                 -   d. Repeat steps (a)-(c) a total of three times.                 -   e. Dry cells in an oven at 80-100° C. for 48 hours.                 -   f. Grind cells using a mortar/pestle to achieve a                     powder form.             -   9) Mix 5% w/w of dry cell powder with the ground rock                 material.             -   10) When this particular rock material+cell powder                 mixture is applied to agricultural soils, the irrigation                 or rainfall will re-apply moisture and allow the                 pre-protonated, re-wet biomass to release their protons.                 This will ultimately induce a local acidity effect on                 the rock particle (molecular) level to accelerate rock                 crystal lattice breakdown. The cells act as                 biodegradable transporters that are also benign to the                 natural soil environment. 

What is claimed is:
 1. A mineral amendment for enhanced rock weathering comprising: an agglomerated silicate mineral having an average particle size of about 0.5 mm to about 3 mm, the agglomerated silicate mineral comprising a comminuted silicate mineral and a binder; and immobile trace elements, the immobile trace elements comprising one or more rare earth elements, rare metals, and transition metals.
 2. The mineral amendment of claim 1, wherein: the rare earth elements comprise scandium (Sc), yttrium (Y), lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), samarium (Sm), europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), and lutetium (Lu); the rare metals comprise beryllium (Be), cesium (Cs), gallium (Ga), germanium (Ge), hafnium (Hf), niobium (Nb), rubidium (Rb), tantalum (Ta), titanium (Ti), vanadium (V), and zirconium (Zr); and the transition metals comprise nickel (Ni), chromium (Cr), and zinc (Zn).
 3. The mineral amendment of claim 1, wherein the immobile trace elements are enriched in abundance compared to their abundance in naturally found silicate mineral.
 4. The mineral amendment of claim 1, wherein the comminuted silicate mineral is forsterite (Mg₂SiO₄) or blast furnace slag.
 5. The mineral amendment of claim 1, wherein the comminuted silicate mineral has an average particle size between about 80 μm and about 100 μm.
 6. The mineral amendment of claim 1 further comprises a slow-release acidifier.
 7. The mineral amendment of claim 6, wherein the slow-release acidifier comprises one or more of gibbsite (Al(OH)₃) or gypsum (CaSO₄)-2H₂O).
 8. The mineral amendment of claim 1 further comprises one or more of zinc, a nutrient, and a biological-derived component.
 9. The mineral amendment of claim 1 is applied to soil to enhance rock weathering.
 10. The soil of claim 9, wherein the amount of CO₂ removed by the mineral amendment can be verified by measuring the immobile trace elements. 